CAPM Calculator
This calculator estimates the expected return on an investment using the Capital Asset Pricing Model (CAPM). Enter the required inputs below to calculate the expected return based on systematic risk.
Enter CAPM Inputs
Understanding the CAPM Formula
What is CAPM?
The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. It is widely used in finance to price risky securities and generate expected returns.
CAPM Formula
The core CAPM formula is:
Re = Rf + β × (Rm - Rf)
Where:
- Re = Expected return on the investment
- Rf = Risk-free rate (return on a theoretically riskless asset)
- β = Beta (measure of the investment's volatility relative to the market)
- Rm = Expected return of the market
- (Rm - Rf) = Market risk premium (additional return expected from the market over the risk-free rate)
Interpreting Beta (β)
- β = 1: The asset moves with the market (average risk)
- β > 1: The asset is more volatile than the market (higher risk)
- β < 1: The asset is less volatile than the market (lower risk)
- β = 0: The asset's returns are uncorrelated with the market
- β < 0: The asset moves inversely to the market (rare)
CAPM Calculation Examples
Click on an example to see the step-by-step calculation:
Example 1: Typical Stock
Scenario: Calculate expected return for a stock with average market risk.
1. Inputs: Rf = 2.5%, β = 1.0, Rm = 8.0%
2. Formula: Re = Rf + β × (Rm - Rf)
3. Calculation: Re = 2.5 + 1.0 × (8.0 - 2.5) = 2.5 + 5.5
4. Result: Re = 8.0%
Conclusion: With β=1 (market average risk), expected return equals the market return.
Example 2: High-Risk Tech Stock
Scenario: A volatile tech stock with β=1.8.
1. Inputs: Rf = 3.0%, β = 1.8, Rm = 10.0%
2. Formula: Re = Rf + β × (Rm - Rf)
3. Calculation: Re = 3.0 + 1.8 × (10.0 - 3.0) = 3.0 + 12.6
4. Result: Re = 15.6%
Conclusion: Higher β demands higher expected return to compensate for risk.
Example 3: Defensive Utility Stock
Scenario: A stable utility stock with β=0.6.
1. Inputs: Rf = 2.0%, β = 0.6, Rm = 9.0%
2. Formula: Re = Rf + β × (Rm - Rf)
3. Calculation: Re = 2.0 + 0.6 × (9.0 - 2.0) = 2.0 + 4.2
4. Result: Re = 6.2%
Conclusion: Lower β means lower expected return than the market.
Example 4: Negative Beta Asset
Scenario: A rare asset with β=-0.5 (moves inversely to market).
1. Inputs: Rf = 1.5%, β = -0.5, Rm = 7.0%
2. Formula: Re = Rf + β × (Rm - Rf)
3. Calculation: Re = 1.5 + (-0.5) × (7.0 - 1.5) = 1.5 - 2.75
4. Result: Re = -1.25%
Conclusion: Negative β can result in negative expected returns.
Example 5: Comparing Two Stocks
Scenario: Compare expected returns for Stock A (β=1.2) and Stock B (β=0.8).
1. Common Inputs: Rf = 2.0%, Rm = 8.0%
2. Stock A (β=1.2): Re = 2.0 + 1.2 × (8.0 - 2.0) = 2.0 + 7.2 = 9.2%
3. Stock B (β=0.8): Re = 2.0 + 0.8 × (8.0 - 2.0) = 2.0 + 4.8 = 6.8%
Conclusion: Higher β stock (A) has higher expected return (9.2% vs 6.8%).
Example 6: Zero Risk-Free Rate
Scenario: Theoretical case with Rf=0%.
1. Inputs: Rf = 0%, β = 1.5, Rm = 10.0%
2. Formula: Re = 0 + 1.5 × (10.0 - 0)
3. Result: Re = 15.0%
Conclusion: Without risk-free rate, return depends entirely on market premium.
Example 7: Low Beta, High Market Return
Scenario: Conservative investment in a bullish market.
1. Inputs: Rf = 1.0%, β = 0.7, Rm = 15.0%
2. Formula: Re = 1.0 + 0.7 × (15.0 - 1.0) = 1.0 + 9.8
3. Result: Re = 10.8%
Conclusion: Even with low β, high market returns boost expected return.
Example 8: High Beta in Bear Market
Scenario: Risky stock when market returns are low.
1. Inputs: Rf = 3.0%, β = 2.0, Rm = 4.0%
2. Formula: Re = 3.0 + 2.0 × (4.0 - 3.0) = 3.0 + 2.0
3. Result: Re = 5.0%
Conclusion: High β doesn't guarantee high returns if market premium is small.
Example 9: Risk-Free Rate Equal to Market Return
Scenario: Unusual case where Rf = Rm.
1. Inputs: Rf = 5.0%, β = 1.2, Rm = 5.0%
2. Formula: Re = 5.0 + 1.2 × (5.0 - 5.0) = 5.0 + 0
3. Result: Re = 5.0%
Conclusion: When market offers no premium, expected return equals risk-free rate.
Example 10: Beta of Zero (Riskless Asset)
Scenario: Asset with no market correlation (β=0).
1. Inputs: Rf = 2.0%, β = 0, Rm = 10.0%
2. Formula: Re = 2.0 + 0 × (10.0 - 2.0) = 2.0 + 0
3. Result: Re = 2.0%
Conclusion: With β=0, expected return equals risk-free rate regardless of market.
Frequently Asked Questions about CAPM
1. What does CAPM stand for?
CAPM stands for Capital Asset Pricing Model, a financial model that describes the relationship between systematic risk and expected return for assets.
2. What is the risk-free rate (Rf)?
The risk-free rate is the theoretical return of an investment with zero risk, typically represented by short-term government bonds (e.g., 10-year U.S. Treasury yield).
3. How is beta (β) calculated?
Beta is calculated using regression analysis of the asset's returns against market returns. A β of 1 means the asset moves with the market, while β>1 indicates higher volatility.
4. What is a good expected return (Re)?
A "good" return depends on the investment's risk (β). Higher β investments should have higher expected returns to compensate for increased risk.
5. Can CAPM be used for any investment?
CAPM works best for publicly traded stocks with measurable β. It's less reliable for private companies, real estate, or assets without market correlation data.
6. What are the limitations of CAPM?
- Assumes markets are perfectly efficient
- Relies on historical data for β which may not predict future risk
- Doesn't account for unsystematic (company-specific) risk
7. Why might two stocks with the same β have different actual returns?
Actual returns may differ due to company-specific factors (management, products) not captured by β, or because β is estimated from historical data that may not reflect current conditions.
8. How often should I update my CAPM inputs?
Regularly update:
- Rf: When risk-free rates change significantly
- β: Quarterly or annually as volatility changes
- Rm: When market expectations change
9. What does a negative β mean?
A negative β suggests the asset moves inversely to the market (rare). Gold and some hedge funds sometimes exhibit negative β.
10. How is CAPM used in practice?
Applications include:
- Valuing stocks by discounting expected cash flows
- Determining hurdle rates for projects
- Constructing efficient portfolios
- Performance evaluation (comparing actual vs. expected returns)
